LMFDB - Newform search results

Refine search

Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
		Only for weight 1:

				Sort order	Select

Results (1-50 of 96 matches)

Next Download displayed columns for results to

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1225.1.g.a	$1225$	$1$	1225.g	5.c	$4$	$2$	$1$	$0.611$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-35}) $	$\Q(\sqrt{5}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{4}+iq^{9}+q^{11}-q^{16}-iq^{29}+\cdots$
1225.1.g.b	$1225$	$1$	1225.g	5.c	$4$	$4$	$2$	$0.611$	$\Q(i, \sqrt{6})$	$D_{6}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+2\beta _{2}q^{4}-\beta _{3}q^{8}+\beta _{2}q^{9}+\cdots$
1225.1.i.a	$1225$	$1$	1225.i	7.d	$6$	$2$	$1$	$0.611$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}-q^{8}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{11}+\cdots$
1225.1.i.b	$1225$	$1$	1225.i	7.d	$6$	$2$	$1$	$0.611$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}+q^{8}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{11}+\cdots$
1225.1.j.a	$1225$	$1$	1225.j	35.i	$6$	$4$	$2$	$0.611$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{3}q^{8}+\zeta_{12}^{2}q^{9}+\cdots$
1225.1.q.a	$1225$	$1$	1225.q	35.l	$12$	$4$	$1$	$0.611$	$\Q(\zeta_{12})$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-35}) $	$\Q(\sqrt{5}) $		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}q^{4}-\zeta_{12}^{5}q^{9}+\zeta_{12}^{4}q^{11}+\cdots$
1225.1.q.b	$1225$	$1$	1225.q	35.l	$12$	$8$	$2$	$0.611$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-7}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$3^{2}$		$q+(\zeta_{24}^{5}+\zeta_{24}^{9})q^{2}+(-\zeta_{24}^{2}-\zeta_{24}^{6}+\cdots)q^{4}+\cdots$
1225.2.a.a	$1225$	$2$	1225.a	1.a	$1$	$1$	$1$	$9.782$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}-2q^{6}-2q^{9}+\cdots$
1225.2.a.b	$1225$	$2$	1225.a	1.a	$1$	$1$	$1$	$9.782$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{6}+3q^{8}-2q^{9}+\cdots$
1225.2.a.c	$1225$	$2$	1225.a	1.a	$1$	$1$	$1$	$9.782$	$\Q$	$_{}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q-q^{2}-q^{4}+3q^{8}-3q^{9}+4q^{11}+\cdots$
1225.2.a.d	$1225$	$2$	1225.a	1.a	$1$	$1$	$1$	$9.782$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{6}+3q^{8}-2q^{9}+\cdots$
1225.2.a.e	$1225$	$2$	1225.a	1.a	$1$	$1$	$1$	$9.782$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-2q^{9}-3q^{11}-2q^{12}+\cdots$
1225.2.a.f	$1225$	$2$	1225.a	1.a	$1$	$1$	$1$	$9.782$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{6}-3q^{8}-2q^{9}+\cdots$
1225.2.a.g	$1225$	$2$	1225.a	1.a	$1$	$1$	$1$	$9.782$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}-3q^{8}-2q^{9}+\cdots$
1225.2.a.h	$1225$	$2$	1225.a	1.a	$1$	$1$	$1$	$9.782$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$-3$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+2q^{4}-6q^{6}+6q^{9}+\cdots$
1225.2.a.i	$1225$	$2$	1225.a	1.a	$1$	$1$	$1$	$9.782$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$2$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-2q^{6}-2q^{9}+\cdots$
1225.2.a.j	$1225$	$2$	1225.a	1.a	$1$	$1$	$1$	$9.782$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$3$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+2q^{4}+6q^{6}+6q^{9}+\cdots$
1225.2.a.k	$1225$	$2$	1225.a	1.a	$1$	$2$	$2$	$9.782$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$-2$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(-1-\beta )q^{3}+(1-2\beta )q^{4}+\cdots$
1225.2.a.l	$1225$	$2$	1225.a	1.a	$1$	$2$	$2$	$9.782$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$0$	$-2$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2\beta q^{3}-q^{4}-2\beta q^{6}+3q^{8}+\cdots$
1225.2.a.m	$1225$	$2$	1225.a	1.a	$1$	$2$	$2$	$9.782$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$-2$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1+\beta )q^{3}+(1-2\beta )q^{4}+\cdots$
1225.2.a.n	$1225$	$2$	1225.a	1.a	$1$	$2$	$2$	$9.782$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-2+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
1225.2.a.o	$1225$	$2$	1225.a	1.a	$1$	$2$	$2$	$9.782$	$\Q(\sqrt{21}) $	$_{}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$1$	$-1$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q-\beta q^{2}+(3+\beta )q^{4}+(-5-2\beta )q^{8}+\cdots$
1225.2.a.p	$1225$	$2$	1225.a	1.a	$1$	$2$	$2$	$9.782$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{3}+(2-\beta )q^{6}-2\beta q^{8}+\cdots$
1225.2.a.q	$1225$	$2$	1225.a	1.a	$1$	$2$	$2$	$9.782$	$\Q(\sqrt{5}) $	$_{}$	$\Q(\sqrt{-35}) $	None	✓	$4$	$1$	$0$	$0$	$0$	$0$	$+$	$2$	$N(\mathrm{U}(1))$	$q-\beta q^{3}-2q^{4}+2q^{9}-3q^{11}+2\beta q^{12}+\cdots$
1225.2.a.r	$1225$	$2$	1225.a	1.a	$1$	$2$	$2$	$9.782$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1-\beta )q^{3}+(-2+\beta )q^{6}-2\beta q^{8}+\cdots$
1225.2.a.s	$1225$	$2$	1225.a	1.a	$1$	$2$	$2$	$9.782$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{3}+(2+\beta )q^{4}+4q^{6}+\cdots$
1225.2.a.t	$1225$	$2$	1225.a	1.a	$1$	$2$	$2$	$9.782$	$\Q(\sqrt{21}) $	$_{}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+\beta q^{2}+(3+\beta )q^{4}+(5+2\beta )q^{8}-3q^{9}+\cdots$
1225.2.a.u	$1225$	$2$	1225.a	1.a	$1$	$2$	$2$	$9.782$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(2-2\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
1225.2.a.v	$1225$	$2$	1225.a	1.a	$1$	$2$	$2$	$9.782$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2\beta q^{3}-q^{4}-2\beta q^{6}-3q^{8}+\cdots$
1225.2.a.w	$1225$	$2$	1225.a	1.a	$1$	$3$	$3$	$9.782$	3.3.257.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-3$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots$
1225.2.a.x	$1225$	$2$	1225.a	1.a	$1$	$3$	$3$	$9.782$	3.3.257.1	$_{}$	None	None	✓	$1$	$0$	$-1$	$3$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots$
1225.2.a.y	$1225$	$2$	1225.a	1.a	$1$	$3$	$3$	$9.782$	3.3.257.1	$_{}$	None	None	✓	$1$	$1$	$1$	$-3$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots$
1225.2.a.z	$1225$	$2$	1225.a	1.a	$1$	$3$	$3$	$9.782$	3.3.257.1	$_{}$	None	None	✓	$1$	$0$	$1$	$3$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots$
1225.2.a.ba	$1225$	$2$	1225.a	1.a	$1$	$4$	$4$	$9.782$	$\Q(\sqrt{2}, \sqrt{5})$	$_{}$	None	None	✓	$2$	$1$	$-6$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+\beta _{1}q^{3}+3\beta _{2}q^{4}+\cdots$
1225.2.a.bb	$1225$	$2$	1225.a	1.a	$1$	$4$	$4$	$9.782$	$\Q(\zeta_{24})^+$	$_{}$	None	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}-\beta _{1}q^{3}+4q^{4}+3\beta _{2}q^{6}+\cdots$
1225.2.a.bc	$1225$	$2$	1225.a	1.a	$1$	$4$	$4$	$9.782$	$\Q(\sqrt{2}, \sqrt{5})$	$_{}$	None	None	✓	$2$	$0$	$6$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}+\beta _{1}q^{3}+3\beta _{2}q^{4}+(2\beta _{1}+\cdots)q^{6}+\cdots$
1225.2.b.a	$1225$	$2$	1225.b	5.b	$2$	$2$	$2$	$9.782$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{2}+3iq^{3}-2q^{4}-6q^{6}-6q^{9}+\cdots$
1225.2.b.b	$1225$	$2$	1225.b	5.b	$2$	$2$	$2$	$9.782$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{2}-3iq^{3}-2q^{4}+6q^{6}-6q^{9}+\cdots$
1225.2.b.c	$1225$	$2$	1225.b	5.b	$2$	$2$	$2$	$9.782$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+iq^{2}+q^{4}+3iq^{8}+3q^{9}+4q^{11}+\cdots$
1225.2.b.d	$1225$	$2$	1225.b	5.b	$2$	$2$	$2$	$9.782$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{3}+2q^{4}+2q^{9}-3q^{11}-2iq^{12}+\cdots$
1225.2.b.e	$1225$	$2$	1225.b	5.b	$2$	$4$	$4$	$9.782$	$\Q(i, \sqrt{21})$	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$5$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+(-4+\beta _{2})q^{4}+(-2\beta _{1}+\beta _{3})q^{8}+\cdots$
1225.2.b.f	$1225$	$2$	1225.b	5.b	$2$	$4$	$4$	$9.782$	$\Q(i, \sqrt{17})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(-3+\beta _{3})q^{4}+\cdots$
1225.2.b.g	$1225$	$2$	1225.b	5.b	$2$	$4$	$4$	$9.782$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}q^{2}-\zeta_{8}^{2}q^{3}+(-1-\zeta_{8}^{3})q^{4}+\cdots$
1225.2.b.h	$1225$	$2$	1225.b	5.b	$2$	$4$	$4$	$9.782$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{3}+(-1-\zeta_{8}^{3})q^{4}+\cdots$
1225.2.b.i	$1225$	$2$	1225.b	5.b	$2$	$4$	$4$	$9.782$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{2})q^{3}+(-2-\zeta_{8}^{3})q^{6}+\cdots$
1225.2.b.j	$1225$	$2$	1225.b	5.b	$2$	$4$	$4$	$9.782$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}^{2}q^{2}+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+(2+\zeta_{8}^{3})q^{6}+\cdots$
1225.2.b.k	$1225$	$2$	1225.b	5.b	$2$	$4$	$4$	$9.782$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(2\beta _{1}+2\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
1225.2.b.l	$1225$	$2$	1225.b	5.b	$2$	$6$	$6$	$9.782$	6.0.4227136.2	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-\beta _{3}+\beta _{4})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$
1225.2.b.m	$1225$	$2$	1225.b	5.b	$2$	$6$	$6$	$9.782$	6.0.4227136.2	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{3}-\beta _{4})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$
1225.2.b.n	$1225$	$2$	1225.b	5.b	$2$	$8$	$8$	$9.782$	8.0.40960000.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{2}-\beta _{3})q^{2}+(-\beta _{5}+\beta _{7})q^{3}+\cdots$

Next Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 96 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.